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  • If the circles <img alt="\mathrm{(x-a)^{2}+(y-b)^{2}=c^{2}\: and \: (x-b)^{2}+(y-a)^{2}=c^{2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28x-a%29%5E%7B2%7D&plus;%28y-b%

If the circles \mathrm{(x-a)^{2}+(y-b)^{2}=c^{2}\: and \: (x-b)^{2}+(y-a)^{2}=c^{2}} touch each other then

Option: 1

\mathrm{a=b \pm 2 c}


Option: 2

\mathrm{a=b \pm \sqrt{2} c}


Option: 3

\mathrm{a=b \pm c}


Option: 4

none of these


Answers (1)

best_answer

The circles will touch each other

\therefore c_{1} c_{2}=r_{1}+r_{2} \Rightarrow a=b \pm 2 \sqrt{c}

Hence (B) is the correct answer.

Posted by

Ritika Harsh

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